Eratosthenes Determines the Size of the Earth in about 200 B.C.

Transcription

1 Eratosthenes Determines the Size of the Earth in about 200 B.C. Sun's rays Syene Alexandria N S 7.2 o Earth

2 He knows the distance between the two cities is 5000 "stadia". From geometry then, 7.2 o 5000 stadia = 360 o Earth's circumference => circumference is 250,000 stadia, or 40,000 km. So radius is: 40,000 km 2π = 6366 km (very close to modern value, 6378 km!)

3 Celestial Navigation

4 Outline Constellations Coordinate Systems Celestial Sphere Precession Seasons Apparent Motions of the Sun

5 What s Up? Stars: 88 Constellations, about 3000 stars visible (by eye) at any time Sun: Does it appear to move? On the same path from day to day? Moon: Does it always look the same? Planets: Do they stay put? Which ones can we see without a telescope?

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7 On modern star charts, all stars are contained in some constellation on the sky here is Orion: 88 constellations officially recognized by the International Astronomical Union (IAU). But are the stars really all together in space? (Recall: lightyear is the distance light travels in one year, or 9.46 x km, or 63,240 AU. Speed of light is 3 x 10 5 km/s.)

8 Star patterns can help you find your way around the sky. Note: angular distance between Polaris and Spica is about 100, so this is a big chunk of the sky. Consult the star charts in your book!

9 An asterism is a star pattern that is not classified as a constellation.

10 The Summer Triangle

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12 The Winter Triangle

13 Why do we see different constellations at different times? Two reasons: 1. Over the night, diurnal motion, due to the rotation of the Earth. Earth rotates from west to east, so sky appears to rotate from east to west. Stars rise and set. Stars appear as trails due to diurnal motion. The trails are called diurnal circles.

14 Circumpolar stars and constellations never rise or set. In the northern sky, circles are centered on a point close to Polaris, the Pole Star. Q: where are these stars during the day?

15 2. Over the year, the nighttime side of Earth gradually turns toward different parts of the sky, so different constellations are visible during the course of the year. These constellations are nearly overhead at midnight local time here for the months shown. So why would it be tricky to try and observe Cygnus from Albuquerque in January or February? Note: this drawing is not to scale!!!

16 Astronomical coordinate systems Purpose: to locate astronomical objects on the sky The sky is a two-dimensional surface, a sphere above our heads. We use an angular coordinate system to locate objects on a sphere

17 How do we locate spots on Earth? Ignoring altitude, to describe a location on the surface of the Earth we use a set of numbers (in degrees) called coordinates: Longitude Latitude

18 0º Position in degrees: Longitude: connecting the poles, 360º, or 180º East and 180º West. 0 at Greenwich, England 90º N Latitude: parallel to the equator, 0-90º N and 0-90º S 0º A location is the intersection of a longitude and latitude line 90º S Albuquerque: 35º05' N, 106º39' W"

19 The Celestial Sphere Same idea when we describe the position of a celestial object The Sun, the Moon and the stars are so far away that we cannot perceive their distances - no depth perception. Instead, the objects appear to be projected onto a giant, imaginary sphere of arbitrary radius centered on the Earth. The celestial sphere is fixed to the stars, so it appears to rotate as Earth (actually) rotates By setting up a coordinate system on this sphere, we can say where to point our telescopes to find an object.

20 The celestial equator is the projection onto the celestial sphere of the Earth s equator. The Earth's poles extend and intersect with the celestial sphere as the north celestial pole and the south celestial pole. To locate an object, two numbers (in degrees), like longitude and latitude are sufficient. Question: why is this view totally imaginary?

21 The zenith is the point directly overhead (cf. nadir). The view from our latitude: The horizon delimits the portions of the sky we can and can t see at any given time. The meridian is the north-south circle that passes through the zenith and both celestial poles. Cardinal directions Over the course of a night, the celestial sphere appears to rotate around us. Question: what does A.M. mean? P.M.?

22 Circumpolar stars never set (or rise). This picture is taken from Australia, at about -35 south latitude. Can astronomers ever see Polaris from this observatory? Is there a southern pole star?

23 (Note: you have to be at a latitude less than 30 N to see the Southern Cross)

24 Celestial Coordinates The imaginary Celestial Sphere is what astronomers use to define positions of objects in the sky. Angular coordinates on the sphere tell us in what direction to look to see a particular star, or galaxy, etc. Two coordinate systems worth mentioning, but astronomers mainly use the second one we'll talk about

25 The Horizon Coordinate System Altitude Angle above the horizon 0-90º The altitude of the north celestial pole equals the observer's latitude on Earth. Useful for navigation! Azimuth Angle measured eastward along horizon, starting from the north 0-360º Az/Alt demonstrator Meridian

26 Pros and cons of the horizon system Pros Easy to understand Cons At different position on the Earth, the same object has different coordinates At different times, the same object has different coordinates The coordinates of an object change in the horizon system!

27 The Equatorial coordinate system A system in which the coordinates of stars and galaxies do NOT change for observers at different locations on Earth (well, almost more later) The coordinates are called Right Ascension and Declination, and are analogous to longitude and latitude on Earth. The equatorial coordinate system is fixed to the celestial sphere.

28 Declination (Dec) is a set of imaginary lines parallel to the celestial equator. Declination is the angular distance north or south of the celestial equator. Defined to be 0 at the celestial equator, 90 at the north celestial pole, and -90 at the south celestial pole. Right ascension (RA): imaginary lines that connect the celestial poles. Right ascension is the angular distance eastward from the vernal equinox. Vernal equinox is the point on the celestial equator the Sun crosses on its march north - the start of spring in the northern hemisphere (cp. Greenwich 0 longitude). More on this later.

29 Declination (Dec) is measured in degrees, arcminutes, and arcseconds. 0 to +90 in north, and 0 to -90 in south. (Also can see N and S nomenclature) Right ascension (RA) is measured in units of time: hours, minutes, and seconds. Ranges 0h 24h This stresses that the sky is rotating over us as time passes, making changes in the sky more meaningful to observers. Nebraska RA-Dec demonstrator

30 Example 1: The star Regulus has coordinates RA = 10 h 08 m 22.2 s Dec = 11 58' 02" Example 2: If a star with RA of 23 h is overhead at midnight, then a star with RA of 22 h would have been overhead an hour earlier. Example 3: In Albuquerque, our zenith is at Dec=35, and an RA that is always changing Hands-on celestial spheres

31 Caution: a star s RA and Dec change slowly with time due to "precession" of the Earth. Celestial coordinates are exactly right for only one instant in time. Astronomers use "epochs", generally now 2000, to make sure everyone s using the same reference frame! The coordinates given for Regulus are for epoch 2000.

32 Precession The direction where the Earth s poles point isn t always the same the Earth is wobbling like a top. Why? Due to the gravitational pull of the Sun and the Moon on the non-spherical Earth. The Earth has an equatorial bulge It is a little fatter across the equator than around the poles. (Diameter difference is 43 km out of 12,756 km)

33 The gravitational pull of Sun and Moon on Earth s equatorial bulge causes the poles to trace out a circle, like a spinning, wobbling top. This is "precession".

34 So the north celestial pole slowly traces out a circle among the northern constellations. It takes 26,000 years to trace out one circle. Polaris won t always be our "pole star"! Most of the time we don t have one! Thus RA and Dec coordinates, which are tied to the positions of the celestial poles and celestial equator, change slowly with time.

35 What causes the seasons? The Earth s axis of rotation is tilted with respect to the plane of the Earth s orbit around the Sun. Rotation axis inclined 23.5 away from the perpendicular to the orbital plane. => This causes solar illumination and number of daylight hours to vary at any location throughout the year.

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37 When the Sun is higher in the sky (summer), energy is concentrated, and ground heats up. When the Sun is lower (winter), its energy is more diffuse, and ground stays cooler. Also, there are more hours of daylight in the summer, making it hotter.

38 My Solar Energy production is best around June 21

39 Vernal equinox is the point on the celestial equator the Sun crosses on its march north - the start of spring in the northern hemisphere. Vernal equinox

40 Erroneous explanation of seasons Some think seasons are caused by the Earth being closer or farther away from the Sun. Not true, because: When it is summer in the northern hemisphere, there is winter in the southern The Earth's orbit is almost a circle The Earth is closest to the Sun in January

41 More on Sun s apparent motion as seen from Earth The Ecliptic Because of the tilt of the Earth's rotation axis, the Sun seems to travel on a path on the celestial sphere, the ecliptic, which is tilted 23.5 with respect to the celestial equator. It appears to us that the Sun travels around the Celestial Sphere once a year. A parallax effect: as we orbit Sun, it is projected against different stars. After 1 year, it returns to same position relative to the stars (ecliptic sim)

42 Equinoxes The 2 intersections of the celestial equator and the ecliptic are called the equinoxes. (Equinoctis = equal nights) Day and night are 12 hours long when the Sun passes through these points

43 Solstices and Equinoxes In March, the Sun moves northward across the celestial equator - at the vernal equinox (recall this defines 0 h RA). In September, the Sun moves southward across the celestial equator - at the autumnal equinox. The summer and winter solstices occur at the northernmost and southernmost points of the ecliptic.

44 Apparent path of the Sun over the day at different times of year Sun s motion demonstrator

45 Change in length of day for people at high latitudes is quite dramatic! Above Arctic Circle, Sun never sets for some days in summer.

46 The Zodiac As the Sun moves along the Ecliptic it passes through 12 constellations known as the Zodiac Ecliptic (Zodiac) simulator

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48 Distance and Brightness Distance to Deneb 3230 light-years Distance to Vega 25 light-years Distance to Altair 168 light-years But they appear almost as bright - Deneb must be superluminous.

49 Aside: A closer look You are not required to know the following details for the exams but hopefully you will appreciate what s involved in the relation between horizontal and equatorial coordinates. Problem: I've got the RA and Dec coordinates for my favorite object, but where is it really on the sky tonight?

50 The easy way Find a close constellation that you can easily recognize. Estimate the offset in degrees from your favorite source. Use the telescope dial (or your hands and fingers) to locate your source on the sky when you have identified the constellation.

51 The accurate way P = North Pole Z = zenith X = location of object α = RA δ = Dec A = azimuth a = altitude φ = observer's latitude φ

52 Given α, we have H = RA of meridian-ra of object, convert H to degrees (multiply by 15). Now we want azimuth A and altitude a. The cosine rule: cos(90 -a) = cos(90 -δ)cos(90 -φ) + sin(90 -δ)sin(90 -φ)cos(h) which simplifies to: sin(a) = sin(δ) sin(φ) + cos(δ)cos(φ)cos(h) φ The sine rule: sin(360 -A)/sin(90 -δ) = sin(h)/sin(90 -a) which simplifies to: -sin(a)/cos(δ) = sin(h)/cos(a) sin(a) = - sin(h) cos(δ)/cos(a)

53 Recommendations Use a computer software program, either something that comes with your telescope or something separate Use the Astronomical Almanac, or similar

54 Direction of the Sun during different seasons